Question: Solve for $x$ : $2x^2 + 2x - 60 = 0$
Answer: Dividing both sides by $2$ gives: $ x^2 + {1}x {-30} = 0 $ The coefficient on the $x$ term is $1$ and the constant term is $-30$ , so we need to find two numbers that add up to $1$ and multiply to $-30$ The two numbers $6$ and $-5$ satisfy both conditions: $ {6} + {-5} = {1} $ $ {6} \times {-5} = {-30} $ $(x + {6}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 6) (x -5) = 0$ $x + 6 = 0$ or $x - 5 = 0$ Thus, $x = -6$ and $x = 5$ are the solutions.